This invention relates to the measurement of the physical properties of tire wall materials and especially measuring the coefficient of radial damping per unit length of tire wall materials. Such coefficient is useful in determining the standing wave characteristics of tires prepared from such materials and the energy loss or rolling resistance of such tires.
A variety of theoretical models have been proposed to explain the behavior of tires. The circular membrane model of Pacejka includes the modeling of a tire crown portion as a circular membrane. From this model, the displacement of a volume element of tire in the radial direction can be characterized by the formula EQU w=C.sub.1 e.sup.AV.sbsp.1.sup..phi. +C.sub.2 e.sup.AV.sbsp.2.sup..phi.( 1)
where ##EQU1## where EQU Z=k.sub.r.sup.2 R.sup.2 -4[npR.sup.2 -(S.sub.o /r.sup.2)][c'-pR.sup.2 ](3)
In these formulae w is the outward displacement of the volume segment, R is the angular velocity of rotation, k.sub.r is the coefficient of radial damping per unit length, n is the fraction of centrifugal force restored by radial force, r is the tire radius, .phi. is the angular coordinate, p is the mass per unit of length, S.sub.o is the tension force on non-rotating tire and AV is the coefficient as defined by Equation (2). It will be appreciated that w is a monotonously decaying function whenever AV.sub.1 and AV.sub.2 are real (i.e. Z is zero or greater) and w will be a sinusoidal function whenever AV.sub.1 or AV.sub.2 are non-real (i.e. Z is less than zero) indicating a standing wave. Heretofore it has been suggested that standing waves be predicted based upon the above formulae by assuming k.sub.r to be sufficiently small that the value of Z may be determined disregarding the factor k.sub.r.sup.2 R.sup.2. It is now believed that k.sub.r is a significant factor in the prediction of standing waves and, by selection of materials and constructions which have higher values of k.sub.r, it is possible to design tires which do not form standing waves at relatively high speeds which can easily be achieved in common vehicles.